Averaging principle for stochastic quasi‐geostrophic flow equation with a fast oscillation

Abstract

AbstractThis work is focused on the quasi‐geostrophic flow equation with a fast oscillation governed by a stochastic reaction–diffusion equation. It derives the well‐posedness of the slow–fast system, in which the fast component is ergodic and the slow component is tight. Applying the averaging principle, it is further proved that there exists a limit process, with respect to the singular perturbing parameter ε, where the fast component is averaged out. Moreover, the slow component of the slow–fast system converges to the solution of the averaged equation in some strong sense as ε tends to zero.